Concepts have been adopted in concept-cognitive learning (CCL) and conceptual clustering for concept classification and concept discovery. However, the standard CCL algorithms are incapable of tackling continuous data directly, and some standard conceptual clustering methods mainly focus on the attribute information, ignoring the object information that is also important to improve clustering analysis and concept classification ability. Therefore, in this article, we present a novel concept learning method, called the fuzzy-based concept learning model (FCLM), to address these two issues by exploiting concept hierarchical relations in concept lattices. More specifically, we first show some new related notions for FCLM based on a regular fuzzy formal decision context; among these notions, the object-oriented and attribute-oriented fuzzy concept similarities are used to achieve the concept similarity measure in concept lattices. Moreover, a novel fuzzy concept learning framework is designed, and its corresponding learning algorithms are developed. Finally, we conduct some experiments on various real-world datasets to demonstrate that the proposed method can achieve the state-of-the-art classification performance among similarity-based learning methods. In addition, we further verify the effectiveness of our method in concept discovery on the MNIST dataset.

In human concept learning, people can naturally combine a handful of labeled data with abundant unlabeled data when they make classification decisions, which is also known as semi-supervised learning (SSL) in machine learning. Especially, human concept learning not only is a static process in human cognition but also can vary gradually with dynamic environments. Nevertheless, the classical SSL algorithms must be redesigned to accommodate newly input data. In this sense, concept-cognitive learning may be a good choice, as it can implement dynamic processes by imitating human cognitive processes. Meanwhile, numerous SSL methods were designed based on the feature vector information of instances, while ignoring concept structural information that is a very important process in human knowledge organization. Based on this idea, a novel SSL method, named semi-supervised concept learning method (S2CL), is proposed for dynamic SSL by employing concept spaces, in which knowledge is represented by hierarchical concept structures. Moreover, to make full use of the global and local conceptual information, we further propose an extended version of S2CL (namely, $\text{S2CL}^{\alpha }$ ) for concept learning. More specifically, to effectively exploit the unlabeled data, this paper first shows some new related theories for S2CL (or $\text{S2CL}^{\alpha }$ ) based on a regular formal decision context; then a novel SSL framework is designed, and its corresponding algorithm is developed. Finally, we conduct some experiments on various datasets to demonstrate the effectiveness of our methods, which include concept classification and incremental learning under a large quantity of unlabeled data.